The equation x^2-2kx+7k-12=0 has real and equal roots. Calculate k !

The roots of the equation  x^2-2kx+7k-12=0 are real and
equal, when the discriminant of the equation, delta, is
zero.

delta = b^2 - 4*a*c, where a,b,c are the coefficients
of the equation.

Let's identify
a,b,c:

a = 1

b =
-2k

c = 7k-12

delta = (-2k)^2
- 4*1*( 7k-12)

delta = 0  => 4k^2 - 28k + 48 =
0

We'll solve the
equation

4k^2 - 28k + 48 =
0

We'll divide by 4:

k^2 - 7k
+ 12 = 0

We'll solve the
quadratic:

k1 =
[7+sqrt(49-48)]/2

k1 =
(7+1)/2

k1 = 4

k2 =
(7-1)/2

k2 =
3

So, the equation will have 2 real equal
roots when k = {3 ; 4}.